MARSShatyt: Compute Expected Value of Y,YY, and YX

Description

Computes the expected value of random variables involving Y for the EM algorithm. This is a base function in the MARSS-package.

Usage

MARSShatyt( MLEobj )

Arguments

MLEobj

A marssMLE object with the par element of estimated parameters, model element with the model description and data.

Value

A list with the following components (n is the number of state processes). Names ending in "T" are estimates from the Kalman smoother; J is also smoother output. Other components are output from the Kalman filter.
ytTEstimates E[Y(t) | Y(1)=y(1)] (n x T matrix).
OtTEstimates E[Y(t)t(Y(t) | Y(1)=y(1)] (n x n x T array).
yxtTEstimates E[Y(t)t(X(t) | Y(1)=y(1)] (n x m x T array).
errorsAny error messages due to ill-conditioned matrices.
ok(T/F) Whether errors were generated.

Details

For state space models, MARSShatyt() computes the expectations involving Y. If Y is completely observed, this entails simply replacing Y with the observed y. When Y is only partially observed, the expectation involves the conditional expectation of a multivariate normal.

References

Holmes, E. E. (2012) Derivation of the EM algorithm for constrained and unconstrained multivariate autoregressive state-space (MARSS) models. Technical report. NOAA Fisheries, Northwest Fisheries Science Center, 2725 Montlake Blvd E., Seattle, WA 98112. Type RShowDoc("EMDerivation",package="MARSS") to open a copy.